LCAO-based theoretical study of PbTiO3 crystal to search for parity and time reversal violating interaction in solids

An experiment towards the search for the interaction of the Schiff moment (S) of the (207)Pb nuclei with electrons in PbTiO3 crystal which violates the time reversal (T) and space parity (P) symmetries was proposed by Mukhamedjanov and Sushkov [Phys. Rev. A 72, 034501 (2005)]. The interpretation of the experiment in terms of the Schiff moment requires knowledge of an electronic density gradient parameter (usually designated as X) on the Pb nucleus in the crystal, which is determined by the electronic structure of the crystal. Here we propose a theoretical approach to calculate the properties in solids which are directly sensitive to the changes of valence electron densities in atomic cores but not in the valence spatial regions (Mössbauer parameters, hyperfine structure (HFS) constants, parameters of T,P-odd Hamiltonians, etc. [L. V. Skripnikov and A. V. Titov, Phys. Rev. A 91, 042504 (2015)]). It involves constructing the crystalline orbitals via the linear combination of atomic orbitals and employs a two-step concept of calculating such properties that was earlier proposed by us for the case of heavy-atom molecules. The application of the method to the PbTiO3 crystal results in the energy shift, Δε=0.82×10(6)S((207)Pb)eaB (3)eV, due to the T,P-odd interactions. The value is compared to the corresponding parameter in diatomic molecules (TlF, RaO, PbO), which have been proposed and used in the past decades in the search for the nuclear Schiff moment. We also present the calculation of the electric field gradient at the Pb nucleus in PbTiO3 for the comparison with other solid-state electronic structure approaches.